Artificial aging control of aluminum alloys

ABSTRACT

The present invention provides a mathematical approach to constructing a model of artificially aging to accurately calculate the value of a property in an aluminum alloy product achieved by aging the alloy. The method includes developing a formula having two independent time and temperature evolving expressions, aging the product to achieve the property by heating the product over an aging period determined by the formula and terminating the heating when the property is achieved according to a mathematical formula. The property is calculated as a function of time and product temperature measured over the aging period. Calculation of the property includes integration of the thermal effects on the product over the entire aging period.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and is a continuation-in-part application of U.S. application Ser. No. 10/294,093 filed on Nov. 13, 2002, the disclosure of which is fully incorporated by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention pertains to artificial aging of aluminum alloy products, particularly to methods of artificially aging aluminum alloy products which include integration of the time and temperature effects on aluminum alloy products over an entire aging process.

2. Prior Art

Production of aluminum alloys includes casting of ingots which may be deformed into wrought products such as rolled plates, forgings or extrusions. The wrought product is solution heat treated by heating to one or more temperatures such as about 800 to 1100° F. to take substantial portions, preferably all or substantially all, of the soluble alloying elements (such as for an Aluminum Association (AA) alloy of the 7xxx series, zinc, magnesium and copper) into solution. After heating to the elevated temperature, the product is rapidly cooled or quenched to complete the solution heat treating procedure. Such cooling may be accomplished by immersion in a suitably sized tank of water or other liquid or by water sprays, although air chilling is usable as supplementary or substitute cooling means for some cooling. After quenching, certain products may be cold worked, such as by stretching or compression where feasible, to relieve internal stresses or straighten the product, even possibly in some products such as those of the AA 2xxx series, to further strengthen the wrought product. For instance, the product may be stretched 1 to 1½% or more, or otherwise cold worked a generally equivalent amount. A solution heat treated (and quenched) product, with or without cold working, is then considered to be in a precipitation-hardenable condition, or ready for artificial aging according to preferred artificial aging methods as herein described or other artificial aging techniques. As used herein, the term “solution heat treat”, unless indicated otherwise, shall be meant to include quenching.

After rapidly quenching, and cold working if desired, the wrought product is artificially aged by heating to an appropriate temperature to improve strength and other properties either alone or in conjunction with other processes such as mechanical or chemical treatment of the product. In one thermal aging treatment, the precipitation hardenable plate alloy product is subjected to two or more main aging steps, although clear lines of demarcation may not exist between each step. It is generally known that ramping up to and/or down from a given or target treatment temperature can itself produce aging effects which can be, and often needs to be, taken into account by integrating such ramping conditions and their precipitation hardening effects along with the main aging steps of the total aging treatment. Such thermal integration is described in greater detail in U.S. Pat. No. 3,645,804 to Ponchel, which is incorporated by reference herein. With ramping and its corresponding integration, two or three steps for thermally treating the plate product according to the aging practice may be effected in a single, programmable furnace and meet the targeted properties for the product.

Aging practices are known to impact the mechanical and physical properties of the product such as strength, fracture toughness and corrosion resistance. Generally, overaged products (products heat treated beyond a peak maximum strength) exhibit improved corrosion resistance and improved fracture toughness at the expense of loss of strength. The strength requirements for the product may be balanced against the need for corrosion resistance of the alloy, particularly for 7xxx series alloys used in aerospace applications which are subjected to corrosive environments.

The aging integration method described in the '804 patent is relevant to predicting the value of alloy strength properties only when the alloy is aged for time periods bringing it into the overaged condition of the aging process and does not accurately predict the value of alloy strength prior to the alloy achieving an overaged state. The portion of the aging process having overaged conditions is represented by the aging data points of FIG. 1 (a plot of tensile yield strength versus time) that are to the right of the peak strength.

The prior thermal integration method of the '804 patent accumulates the time-temperature effects and signals that the aging process is complete for a desired property in the alloy when the accumulated thermal effect reaches a value known to be associated with the desired property in a particular alloy. The integration formula can be expressed as K=∫∫dEdt where K is a predetermined value for the alloy, E is a correction factor for each aging temperature and t is the period of time the alloy is at that temperature. The correction factor E can be expressed as $E = \frac{t_{T}}{t_{T^{\prime}}}$ where t_(T) is the time required to achieve a desired property (e.g., strength) at a target temperature T and t_(T), is the time required to achieve the same property at an arbitrary temperature T′. The E factor increases exponentially with temperature, yet the values of E are determined only for the overaged state of the alloy. No accounting is made for the thermal effects in the portion of the aging process where the alloy is in an underaged state, i.e. to the left side of the peak strength in FIG. 1.

According to the prior art method, aging at target temperatures is performed until the desired value of K is reached, with K having a predetermined correlation with strength. Strength per se is not calculated according to the prior art aging integration method, only the integrated value of K is calculated which is then correlated with strength. The starting point for that method is at the beginning of the overaging portion of an aging process, namely, at peak strength. The thermal effects of heating up an alloy and aging steps imposed before reaching peak strength are not considered. The K value is a measure of change in the thermal effect on the alloy (the time spent at each temperature) after peak strength is achieved and ranges from near zero (at peak strength) to a positive number (at reduced strength from overaging). The K value does not represent an actual property in the alloy.

In an effort to compare the thermal effect (K value) of the prior art method with actual strength, a value of strength for an overaged alloy correlated from calculations of K according to the prior art aging integration method was plotted over time in FIG. 1. The overaged portion of the curve exhibits some similarity to the actual strength of the alloy. According to such a correlation, in the underaged portion of the curve, the K value would be nearly zero and predicted strength would approach a maximum. See the prior art plot in FIG. 1. However, experience shows, as indicated by the data points of measured strength to the left of peak strength in FIG. 1, that yield strength begins low and increases during the underaged state of the alloy to a peak value and then decreases in the overaged portion of the aging process. The difference between the actual tensile yield strength (plotted data) and the tensile yield strength that would be determined based on the correlations used in the prior art model in the underaged portion of the graph represents an inaccuracy in the prior thermal integration method. Not only does the prior art method fail to predict an alloy property (e.g. strength), it does not account for the thermal effects of the entire aging process which includes the underaged portion.

Accordingly, a need remains for a mathematical formula which can be used to integrate all of the thermal effects of artificial aging on properties of aluminum alloys that accounts for the entire artificial aging process (including the underaged portion) and allows for the calculation of properties of aged alloys in the pre-peak aged and proximal to the peak aged and post-peak aged regimes.

SUMMARY OF THE INVENTION

This need is met by the present invention which provides a method for developing a mathematical formula to accurately predict the value of properties in an aluminum alloy from a knowledge of the entire thermal history of the alloy post solution heat treat. The method comprises: deriving a formula which contains two independent time and temperature evolving expressions for the alloy which relate the property to bypass and shear mechanisms in the alloy during an artificial aging process; subjecting an article comprising the alloy for which the formula was derived to an artificial aging process; evaluating the formula for the time and temperature conditions utilized during the artificial aging process; and discontinuing the process at a time indicated by the evaluated formula such that the desired value of the property is achieved in the alloy upon cooling to the ambient temperature. In some embodiments the artificial aging process is carried out at a single temperature and includes correction for heat-up and cool-down time during the aging process. In some embodiments the desired value of the property occurs in the time period corresponding to a time prior to the peak aged value of the property. In some embodiments the desired value of the property occurs in a time period proximal to the peak aged value of the property. In some embodiments the desired value of the property occurs in a time period after the peak aged value of the property.

Some suitable alloy properties for calculating according the present invention include strength (such as longitudinal tensile yield strength), corrosion resistance, hardness, fracture toughness and electrical conductivity. Each of these properties may be represented as the sum of two independently time and temperature evolving expressions, for example the strength of an alloy and may be represented as a normalized (unitless) value of X as X(t,T)=X _(s) −βX _(b) where β is a constant for the alloy, such that X is characterized by two mechanisms X_(s) and X_(b), having behaviors described by the following equations: $\frac{\mathbb{d}Y_{s}}{\mathbb{d}t} = {{n_{s}K_{s}^{1/n_{s}}Y_{s}^{1 - {1/n_{s}}}\quad{where}\quad Y_{s}} = {\ln\left( \frac{1}{1 - X_{s}} \right)}}$ $\frac{\mathbb{d}Y_{b}}{\mathbb{d}t} = {{n_{b}K_{b}^{1/n_{b}}Y_{b}^{1 - {1/n_{b}}}\quad{where}{\quad\quad}Y_{b}} = {\ln\left( \frac{1}{1 - X_{b}} \right)}}$ $K_{s} = {K_{s^{o}}{\exp\left( {- \frac{Q_{s}}{RT}} \right)}}$ $K_{b} = {K_{b^{o}}{\exp\left( {- \frac{Q_{b}}{RT}} \right)}}$ wherein K_(s) ⁰, K_(b) ⁰, Q_(s), Q_(b), n_(s) and n_(b) are experimentally determined constants for the alloy.

The aging step may be terminated when the desired value for X is attained and dX/dt is one of positive (alloy in the underaged state), zero (alloy at peak strength) or negative (alloy in the overaged state). Alternatively, the aging step may be terminated when dX/dt is positive, zero or negative and the desired value for σ is attained according to the following: ${X\left( {t,T} \right)} = \frac{\sigma - \sigma_{w}}{\sigma_{p} - \sigma_{w}}$ where σ_(p) is theoretical maximum strength for the alloy product; and

σ_(w) is the strength of the alloy product prior to the aging step.

The step of terminating aging may include cooling the product during a cooling time period wherein the property continues to change during the cooling time period so that the property is calculated as a function of time and alloy temperature measured over the aging period and the cooling time period.

The present invention further includes a system for artificially aging an aluminum alloy product to achieve a property in the alloy product. The system may have a heating apparatus for heating an alloy product during an aging period and an alloy temperature controller for controlling the temperature of the alloy product in the heating apparatus during the aging period. The controller includes software containing an algorithm for calculating a property of the alloy as a function of time and alloy product temperature measured over the aging period according to the above-described mathematical formulas.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph of an aging curve with models thereof according to the prior art and the present invention;

FIG. 2 is a graph of theoretical aging curves of strength versus time;

FIG. 3 is a graph of theoretical aging curves of normalized strength versus time;

FIG. 4 is a graph of isothermal aging of an AA 7085 series alloy at temperatures of 175-250° F. and best fit curves by the model of the present invention;

FIG. 5 is a graph of isothermal aging of the AA 7085 series alloy at temperatures of 275-330° F. and best fit curves by the model of the present invention;

FIG. 6 is a graph of temperature versus time for an artificially aged AA 7085 series alloy;

FIG. 7 is graph of calculated tensile yield strength versus time for the same alloy; and

FIG. 8 is a graph of rate of change in calculated strength versus time for the same alloy.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is described with reference to a mathematical model to accurately predict the effects of thermal exposure of an aluminum alloy on properties of the alloy which evolve with such exposure. As the term is recognized by those of skill in the art, an alloy article which has been subjected to solution heat treatment, quenching, and residual stress relieving processes or one that has been rapidly cooled following hot working processes are in a condition for benefiting from such thermal exposure, also termed herein as “an artificial aging treatment”. As the term is used herein, artificial aging is performed by bringing an aluminum alloy article to a temperature sufficiently above ambient temperature and holding it there for a time period sufficiently long to produce alteration in the precipitate size and number of the alloy. Artificial aging procedures may include several temperature regimes and “soak” times and may optionally include mechanical working of the alloy during or between artificial aging steps.

In general it is known to artificially age aluminum alloys to improve selected properties. Properties which may be improved by an artificial aging process include strength, for example, tensile yield strength, and the resistance of the alloy to stress corrosion cracking. Other properties which are improved with an aging process which optionally includes mechanical working of the alloy are corrosion resistance, hardness, fracture toughness, and electrical conductivity. Aluminum alloys which are particularly suited to benefit from the present invention include the AA series 2XXX, 6XXX, and 7XXX, including AA 7085. Moreover, the present invention may be applied to alloys in any condition of aging following either solution heat treatment, quenching, and residual stress relief or rapid quenching following hot working. Examples of hot working include rolling, extrusion and forging.

The mathematical model of the present invention can be used to accurately predict properties even when the aging process includes mechanical treatments, for example forming and machining, and chemical treatments, for example, anodizing. Heretofore, mathematical models for predicting the value of properties attained for a given set of artificial aging conditions have assumed that the alloy undergoing aging starts at peak aged strength. Accordingly, these models utilize a single time and temperature evolving variable wherein, with increases in time and/or aging temperature the strength of an article comprised of the alloy decreases. With reference to FIG. 1, the curve labeled “Prior Art”, these models utilize an equation having a single time and temperature evolving variable, which when applied to aging times before peak aging predict a monotonic rise in the strength of the article to a theoretical maximum. In fact, for real aluminum alloy articles, an article made from the alloy does not display such a strength maximum. With reference to FIG. 1, the curve labeled “invention”, the actual strength of an article of a given aluminum alloy displays a slow increase from its solution heat treated strength as artificial aging time progresses at a given temperature. As time passes, the strength passes through a maxima (peak-aged condition) and then decreases with increasing aging time. In general, the effects of increasing temperature shorten the time over which this local maxima is achieved. In part, prior art models fail to account for the fact that properties which evolve with heat treatment of the alloy (artificial aging) evolve due to a number of different physical process occurring over time in the aging alloy as it is maintained at a particular temperature. An example of this is precipitation hardening which occurs during aging and is known to involve different mechanisms of the interaction of dislocations passing through the metal with respect to different sizes of the precipitates present. During averaging, the average size of precipitates is increased and the number of precipitates is known to decrease. Moreover, it is known that dislocations are generated in the aged product under mechanical loading conditions. It is also know that the interaction of dislocations with precipitates effects the properties of the aluminum alloy.

Without being bound by theory, it is believed that many of the properties of aluminum alloys which evolve with aging (treatment of the alloy at an elevated temperature over a given time) are dependent on two separate interaction mechanisms between dislocations and precipitates which are known to effect the properties of a post-aged alloy. These have been termed “shear” and “bypass” mechanisms. These dislocation/precipitate interactions are so termed because during the in service loading conditions, the evolving dislocations either shear through (smaller) precipitates or bypass around (larger) precipitates. Accordingly, the dislocation shear and dislocation bypass contribution to the properties of an alloy are driven by the number and average size of precipitates present in the alloy and by the number of dislocations generated in the alloy. The final properties of the alloy (e.g. strength) after aging are determined at least in part by these two mechanisms (shear and bypass) of interaction with moving dislocations. During heating in the underaged state the number of precipitates increases and the ratio of small to large precipitate likely also increase. In the overaged state the number of precipitates decreases and the ratio of small to large precipitates also decrease. The weight of the contribution of these the shear and bypass mechanisms to the physical properties of an alloy after artificial aging will vary with temperature at which the aging process is carried out and the amount of time the alloy is subjected to the aging process. Accordingly, a mathematical model utilizing a single time and temperature evolving expression to predict the final properties of an alloy from a knowledge of the thermal history of the an alloy can not but fail to accurately predict the change in value of a given property of an artificially aged alloy over the entire regime of time and temperature to which that alloy has been exposed during a post quenched aging process.

In this same vein, a mathematical model utilizing a single time and temperature evolving expression can not but fail to accurately predict the property value because it fails to account for the diametrically opposed manner that the various physical processes occurring during artificial aging effect the property in question. These competing mechanisms are accounted for in the mathematical model of the present invention.

By way of exemplifying the foregoing, the present invention, the strength (a) of an aluminum alloy product (e.g. longitudinal tensile yield strength) may be represented by a normalized strength X which varies as a function of time (t) and temperature (T) and where ${X\left( {t,T} \right)} = {\frac{\sigma - \sigma_{w}}{\sigma_{p} - \sigma_{w}} = {X_{s} - {\beta\quad X_{b}}}}$ where β is a constant for each alloy composition. The subscripts herein refer to the following aspects:

s=shear mode of interaction of precipitates

b=bypass mode of interaction of precipitates

p=theoretical peak

w=W-temper

The W-temper strength of the product to undergo artificial aging is σ_(w) and is measured prior to artificial aging. The maximum attainable strength σ_(p) is the theoretical peak strength for the alloy product, and the minimum strength σ_(∞) is achieved at theoretical infinite aging. These maximum and minimum strengths, σ_(p) and σ_(∞), are constants determined for each particular alloy composition. The total normalized strength X theoretically ranges from 0 to 1 and includes two variables, X_(S) (normalized strength from shear mode) and X_(b) (normalized strength from bypass mode).

The actual strength (a) begins at an initial value of σ_(w). During aging, σ typically reaches a maximum value that may approach σ_(p) and then falls off during averaging. The relationship of σ as a function of time (t) is shown in FIG. 2 for one aging practice. FIG. 3 shows the same data as in FIG. 2 transformed to the normalized strength X as a function of time (t).

The shear component of normalized strength, X_(S), may be expressed as: $X_{s} = \frac{\sigma_{s} - \sigma_{w}}{\sigma_{p} - \sigma_{w}}$

The bypass component of normalized strength, X_(b) is as follows: $X_{b} = \frac{\sigma_{s} - \sigma}{\sigma_{p} - \sigma_{\infty}}$

It should be appreciated by reference to FIG. 3 that for the overaged portion of the curve, X_(S) approaches unity or X=1−βX _(b)

When X_(S) approaches unity, the relationship between tensile yield strength and time is as shown in FIG. 1 for the prior art correlated strength curve. Not only is the prior art correlated curve inaccurate for the underaged portion of the curve (to the left of peak strength), but in the beginning of the overaged portion of the curve (to the right of peak strength), there is a perceptible difference (shown by the hatched region in FIG. 1) between the strength calculated based on conventional practice of focusing only on the overaged state and the actual strength as well as the strength calculated according to the present invention. In contrast, the present invention accounts for the thermal effects prior to the overage conditions for the product by including both evolving variable X_(S) and X_(b).

The constant β may be calculated for a particular alloy composition according to the following equation: $\beta = \frac{\sigma_{p} - \sigma_{\infty}}{\sigma_{p} - \sigma_{w}}$

It has been found that the aging process leading to the formation of precipitates in the alloy in both the underaged and overaged conditions is diffusion controlled and follows Avrami kinetics. This discovery allows X_(S) and X_(b) to be expressed mathematically as functions of time and temperature as follows: $\frac{\mathbb{d}Y_{s}}{\mathbb{d}t} = {{n_{s}K_{s}^{1/n_{s}}Y_{s}^{1 - {1/n_{s}}}\quad{where}\quad Y_{s}} = {\ln\left( \frac{1}{1 - X_{s}} \right)}}$ $\frac{\mathbb{d}Y_{b}}{\mathbb{d}t} = {{n_{b}K_{b}^{1/n_{b}}Y_{b}^{1 - {1/n_{b}}}\quad{where}\quad Y_{b}} = {\ln\left( \frac{1}{1 - X_{b}} \right)}}$

The variables K_(s) and K_(b) are temperature (T) dependent as shown by the following: $K_{s} = {K_{s^{o}}{\exp\left( {- \frac{Q_{s}}{RT}} \right)}}$ $K_{b} = {K_{b^{o}}{\exp\left( {- \frac{Q_{b}}{RT}} \right)}\quad{and}}$ where K_(s) ₀ , K_(b) ₀ , Q_(s), Q_(b), n_(s) and n_(b) are constants for each alloy composition.

Using these equations, a mathematical model is created based on time (t) and temperature (T) beginning with the startup of an aging process to solve for the normalized strength X and the corresponding strength σ.

In addition to β discussed above, for each particular alloy composition, the constants K_(s) _(o) , K_(b) _(o) , Q_(s), Q_(b), n_(s) and n_(b) are experimentally determined. Plots are made of strength σ (e.g., longitudinal tensile yield strength) versus time (t) for various temperatures (T). These data points of σ, t and T are used to generate a best fit curve for all temperatures, i.e., to determine the constants for an alloy composition which allow a best fit of the above-described equations to the data. The constants for that alloy composition are then adopted for subsequent control of artificial aging of the same alloy composition.

Although illustrated herein above for tensile strength, this approach to modeling the aging behavior of various properties may be used to develop expressions which accurately predict the values of other aluminum alloy properties at times in the artificial aging process which correspond to the regime before the peak aging or proximal to the peak aging period, as well as accurately predict the value of the property in the post-peak aging time regime. Accordingly, as illustrated above for tensile strength, such equations may be characterized as having two independently time and temperature evolving expressions, a first expression which evolves in time and temperature that dominates the value of the modeled property in the pre-peak aged regime (shear) and a second expression which evolves independently of the first expression in time and temperature that dominates the value of the modeled property in the post-peak aged regime (bypass), the sum or difference of the two variables (depending upon the form of the expression and the property being modeled) contributing jointly to the aged value of the property. Accordingly, by taking the first derivative with respect to time of such a mathematical expression (FIG. 8), the artificial aging treatment can be compensated for by discontinuing the treatment when the value is positive (pre-peak aged value), zero (at peak aged value) or negative (overaged value) depending upon the desired optimization of other properties in the alloy as calculated from the formula. Moreover, as will be appreciated, such a model permits prediction of property values starting with a sample in any condition of aging so long as the thermal history of the material is known. Additionally, it will be appreciated also that such a model permits accounting for the change in properties that are accompanied by slow heating or cooling cycles experienced in real world furnaces, and thus permits real time compensation by adjusting times and temperatures accordingly. Thus, utilizing a mathematical formula in accordance with the present invention and by monitoring individual article temperature, an artificial aging treatment may be adjusted to achieve a desired value in a particular article within a batch of articles as it experiences the extremes of the normal variability of the equipment used in such treatment methods.

As mentioned above, one feature of the present invention is the ability to determine the end point for an aging practice based on the calculated tensile yield strength. While conventional aging practice dictates stopping heat treatment only after following a predetermined procedure of heating to one or more temperatures for set time periods, the actual tensile yield strength (or other desired property) may not be the targeted value at the end point of the practice.

In one embodiment of the present invention, the temperature of the alloy product and the time spent at each temperature is input to a controller. The controller is equipped with a computer containing software having an algorithm for the alloy undergoing treatment written according to the above-described equations to calculate the tensile yield strength of the product while the heat treatment is ongoing. The software may be programmed to signal that the desired tensile yield strength has been achieved and may automatically institute the next aging step, shut down the furnace, apply cooling air to the products, provide notice to an operator to do so or the like. In this manner, unintended levels of overaged conditions and underaged conditions with the associated undesirable properties in the product may be avoided.

While industrial aging furnaces are designed to heat products uniformly, some temperature variation could also occur between work pieces in a furnace or even within one work piece. Such temperature variance creates, for example, variability in the actual tensile yield strength. In the present invention, the temperature variance is used to calculate the resultant variance in the property, that is, as exemplified above, in the tensile yield strength (σ). The calculated strength a may be used to select work pieces for subsequent use. Certain work pieces in a furnace may have calculated tensile yield strength directly on target and may be used for their intended purpose. Work pieces having calculated strengths outside the target may be identified as being of use in applications where strength is less critical or may even be scrapped. The additional information provided by the present invention allows for screening of work pieces based on their calculated properties.

The present invention may also be used to account for aging which occurs after the product is removed from the furnace. During the period of time that it takes for the product to cool, aging continues at a decreased rate either increasing strength for underaged condition, or decreasing strength for overaged conditions. By continuing to monitor the temperature of product after interruption of the aging process until the product has sufficiently cooled (and artificial aging virtually ceases), the present invention allows for calculation of the modeled property, as exemplified above, in the final tensile yield strength. Alternatively, once the degree of overaging and loss of tensile yield strength during cool down is known, subsequent aging processes may be operated to account therefore. The aging process may be interrupted before the target strength is achieved so that the added impact of aging during cool down results in the target value of the modeled property, as exemplified above, to achieve the desired strength.

Likewise, the thermal effects of the initial step of heating the product up to the desired aging temperature may be accounted for by including the time and temperature data for that portion of the aging process when performing the method of the present invention. The thermal effects of heat-up and cool down between aging steps in a multi-step aging practice may also be accounted for in a similar manner.

In use, the algorithm (also sometime referred to herein for convenience as “the mathematical formula”) may be written to monitor for either σ or X and for a particular slope of the aging curve (e.g. strength vs. time). A typical aging curve as in FIG. 1 may pass through a desired value of the modeled property, for example, a strength value once while the slope of the curve is positive (for the under aging portion) and again while the slope of the curve is negative (during the averaging portion). Overaged product is often desirable for a balance of different properties, for example corrosion resistance and strength; therefore, the endpoint of an aging process incorporating the present invention may be reached, for example a desired strength value at negative slope on the aging curve. In that case, the aging endpoint is reached when X (or σ) is a desired value and dX/dt is negative. The aging endpoint may also be set for conditions when dX/dt is positive or zero. Unlike in conventional aging practice which accounts only for the overaged condition, the present invention is useful for determining the properties of alloys over the entire aging process including both the underaged condition and the peak aged condition.

The W-temper of product may be considered to be a starting point for the artificial aging process. In conventional industrial practice, the tensile yield strength at W-temper (σ_(w)) of the product is measured shortly after quenching and any stretching or compressing steps. However, the product continues to age naturally prior to the onset of the artificial aging process. It has been found that changes in σ_(w) (e.g., of about 7 ksi) do not impact the accuracy of the calculated overage strength σ. For those situations, although σ_(w) has changed slightly, the change to the constant β is minimal and may not warrant refitting the plotted isothermal curves to determine new constants for the alloy composition.

Modifications, intentional or otherwise, to an alloy composition may cause its actual strength to be different from the calculated strength σ. The mathematical model of the present invention may be refitted for the new composition by altering σ_(p) without changing the remaining constants. Hence, it should be appreciated that the present invention is robust for many aluminum alloy production practices.

The present invention is described in reference to modeling and control of the thermal effects of artificial aging on tensile yield strength. However, this is not meant to be limiting. Other properties of an aged aluminum alloy (such as corrosion resistance, hardness, fracture toughness and electrical conductivity) can be calculated according to the present invention wherein the property is modeled according to a mathematical formula as a sum of two independently time and temperature evolving expressions which can be evaluated for the function of time and alloy temperature over the aging period. Such modeling can be used to accurately predict the value attained for the modeled properties even in time periods which includes a time period in which the alloy property is underaged or is proximal to a peak-aged or overaged condition when it has reached a desired property. Other multiple mechanism formulas similar to those described herein with reference to strength may be applicable to these other properties.

Although the invention has been described generally above, the particular examples give additional illustration of the product and process steps typical of the present invention.

EXAMPLE 1 Determine Constants

Six-inch thick plates of W-temper AA 7085 were fabricated in an industrial plant. The plates were rapidly heated to an isothermal soak at temperatures ranging between 175° F. and 330° F. in a laboratory scale furnace. The longitudinal tensile yield strength of the plates was measured over time during the aging processes. FIG. 4 includes plots of aging data (strength vs. time) at 175°, 200° and 250° F., and FIG. 5 includes aging data at 275°, 300°, 310°, 320° and 330° F. The data for each temperature was fitted to the equations described above to determine the constants as listed in Table 1: TABLE 1 Constant Value Constant Value σ_(w) 55.4 ksi K_(b) ^(o) 9.832 × 10¹⁴/sec σ_(p) 76.9 ksi Q_(s)  49,982 J/gmole K σ_(∞) 43.7 ksi Q_(b) 163,450 J/gmole K β 1.546 n_(s) 0.532 K_(s) ^(o) 1.56 × 10³/sec n_(b) 0.933

The curves shown in FIGS. 4 and 5 are the best fits for the data therein using these experimentally determined constants.

EXAMPLE 2 Model

Six-inch thick plates of W-temper AA 7085 were artificially aged according to a conventional aging practice in an industrial furnace. In a two-step process, the plates were brought to about 250° F. in about 7 hours and held for about 6 hours and subsequently heated to about 310° F. and held for 10 hours and then cooled to about 250° F. and held for about 24 hours. Twelve thermocouples measured the temperature of the plates at various locations in the furnace. The resulting time and temperature profile for each of the twelve thermocouples is shown in FIG. 6 which demonstrates the variability in actual temperature experienced by the plates. The actual tensile yield strength was determined experimentally to be 75.6 ksi. Using the mathematical model of the present invention, the tensile yield strength for the plates was calculated and is shown over time in FIG. 7. When the curves for FIG. 1 were initially produced, there was an offset of the calculated final strengths from the actual strength. The offset is believed to be due to an aitifact in using the constants listed above from the laboratory scale aging experiment of Example 1 in the industrial scale aging process of this Example 2. A value of 84.0 ksi for σ_(p), used to produce the curves in FIG. 7 so that the final calculated tensile yield strengths were consistent with the measured strength of 75.6. The variation between 75 and 76 ksi of the calculated strengths is indicative of the variation of actual temperatures of the plates as measured by the thermocouples.

The desired final strength of about 76 ksi occurred first at about 15 hours and again at 25 hours. All the desired properties may not be achieved prior to passing through a point of maximum strength; hence the present invention permits selection of the proper time at which the desired strength and other properties are achieved.

The rate of change of calculated normalized strength X or dX/dt is shown in FIG. 8. The rate of strength change initially increased during the first period of heat-up, decreased between about 5 and 12 hours during the first isothermal treatment stage at about 250° F., increased again during the second heat-up period and finally decreased to below zero between about 14 and 25 hours during the second treatment stage at about 310° F. Negative rate of strength change began at about 17 hours when maximum strength was achieved as evidenced by the peak strength of about 78 ksi shown in FIG. 7. Although this aging process was controlled according to conventional aging practice based on a pattern of predetermined time at temperature, these data demonstrate that the next stage in the aging process could have been instituted based on the calculated strength of about 76 ksi and negative dX/dt, namely at about 23 hours.

Having described the presently preferred embodiments, it is to be understood that the invention may be otherwise embodied within the scope of the appended claims. 

1. A method of artificially aging an aluminum alloy product to achieve a property value in the product wherein said property value varies in response to aging, the method comprising: (i) providing a mathematical formula expressing the property as a sum of two independently time and temperature evolving expressions, wherein a first expression dominates the behavior of the property with aging in the regime before the peak aging value of the property and a second expression dominates the behavior of the property with aging in the regime following the peak aging value of the property; (ii) heating an aluminum alloy over an aging period and terminating the aging period when the property value is achieved in accordance with evaluating over time the mathematical formula provided in step “i” for each temperature regime experienced by said product.
 2. The method of claim 1 wherein the product is optionally age formed during the artificial aging process.
 3. The method of claim 1 wherein the aging period optionally contains a portion during which the temperature of the article is varied and optionally contains a portion during which the temperature of the article is substantially fixed.
 4. The method of claim 1 wherein the aluminum alloy product is solution heat treated prior to aging.
 5. The method of claim 1 wherein the aging period contains periods during which the temperature is varied.
 6. The method of claim 1 wherein the aging period is carried out at a substantially fixed temperature.
 7. The method of claim 1 wherein the alloy article to be aged begins the aging period in an underaged state and the mathematical model accurately predicts the property in an aging period prior to peak aged state, proximal to a peak aged state or following the peak aged state.
 8. The method of claim 1 wherein the property is selected from the group consisting of strength (e.g. tensile yield strength), fracture toughness, corrosion resistance, hardness and electrical conductivity.
 9. The method of claim 1 wherein said time and temperature-domain evolving variables are X_(s) and X_(b) and wherein said time- and temperature-dependent expression of the property comprises X(t,T)=X _(s) −βX _(b) wherein X_(s) relates the value of the property to a dislocation shear mechanism in the alloy and X_(b) relates the value of the property to a dislocation bypass mechanism in the alloy, and β is a constant for the alloy.
 10. The method of claim 9 wherein the aging step is terminated when the desired value for X is attained and the value of dX/dt is selected to be about zero or negative.
 11. The method of claim 1 wherein the alloy is selected from the group consisting of a 2xxx, 6xxx, or 7xxx AA series alloy and AA7085 alloy.
 12. The method of claim 1 wherein the product comprises an aluminum article selected from a rolled article, an extruded article, and a forged article. 